无失真信源编码及其定理ppt课件.ppt

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1、12 ,.,qSS SS12 ,.,rXx xx编码器编码器12:,.,qCWWW信源码字符号集12 ,.,qSS SS12 ,.,rXx xx非奇异码唯一可译码奇异码非惟一可译码NlqrloglogNqlrlogloglqNrNlqrloglqNNq( )loglH SNr( )2loglH SNr( )lH SN等长编码时平均每个信源符号所需的二元码符号的理论极限loglqN信源等概分布时( )log( )loglH SlrNH SNr长为l的码符号序列所能载荷的最大信息量长为N的信源序列平均携带的信息量log( )lrH SNloglRrN ( )( )logH SH SlRrN( )1

2、( )0( )H SH SH S( )iD I s2222( )( )( ) (1)iiD I sD I sNHS 12,31( ),44ssSP s134( )log4log0.811()443H Sbit symbol2221222( )(log)( )3311(log)(log)(0.811)0.47154444iiiiD I sppH S510272250.4715(0.96)4.13 10(0.811) 0.0410N非惟一可译奇异码非惟一可译非奇异码惟一可译非奇异码惟一可译非奇异码所有码非奇异码惟一可译码即时码根：树的最上端树枝的个数为r，r=2为二元码树0100111101001

3、0001码4的树图ABCD中间节点（空心）节点：树枝的终端，从节点生出树枝，每个节点伸出r个枝终端节点（实心）码字：从根到终端节点对应的码符号，又称树叶1212,( ),(),()( )qqsssSP sP sP sP s12,qW WW12, ,ql ll()( )(1,2, )iiP WP siq1( )qiiiLP s l( )(/ )tH SRbit stLtRtRL12,NNqS ()NH SNS( )1( )1( )( )loglogNNrrH SLH SLHSHSrNNrNN或N ( )limNrNLHSN1()NqNiiiLp NLNiN ( )rHS( )H SRL()log

4、NLHSLNrlogRrlogRr( )rHSL( )11rHSL ( )( )rHSH S( )H SL( )H SRL1212,3 41 4( )ssSppP s( )H S 120,1ssL 131( )111()44qiiiP s l 二元码符号 信源符号( )0.811H SLi()iP29331271233()1616161616L 二元码符号 信源符号844. 0322722LL961. 0)(2LSH961. 0)(22LSHR985. 03991. 04)(985. 03二元码符号比特R)(991. 04二元码符号比特R12345678,()0.40.180.10.10.07

5、0.060.050.04XxxxxxxxxP X01001111树图X1:1X2:001000011X3:011X4:0000X5:0100X6:0101X7:00010X8:00011821( )( )log( )2.55(/)iiiH Xp xp x比特 符号)(61. 25)05. 004. 0(4)06. 007. 01 . 0(3) 1 . 018. 0(4 . 0)(81信源符号码符号iiilxpL%7 .9761. 255. 2)(LXH2.55385%L12345,()0.40.20.20.10.1XxxxxxP X0101010101010101511( )0.4 1 0.2

6、 20.2 30.1 40.1 42.2iiiLP s l 521( )0.4 20.2 20.2 20.1 30.1 32.2iiiLP s l 2221() ( )()qiiiiE lLP slL522111( )()1.36iiiP slL522221( )()0.16iiiP slLjkjkppll)()(CLCL1)()()(SHCLSHrr123456,()0.320.220.180.160.080.04XxxxxxxP X621()( )log( )2.35(/)iiiH Xp xp x 比特 符号)(4 . 2)(61信源符号二元码符号iiilxpL%9 .974 . 235.

7、 2)(LXH621()( )log( )2.35(/)iiiH Xp xp x 比特 符号)(4 . 2)(61信源符号二元码符号iiilxpLqaaaA,21kiikikAaaaPaF1,)()(11,)(21)()()(kiikkikAaaaPaPaFSF1234561.02( )F a3( )P a( )kF ai()iP a()kF aka( )( )abF aF b时)(kaFkaS )(kaFka( )kF a( )kF a()()kkl aF alx 1()log1()kkl aP a4321,ssssS )(SF)(SF1)(1log)(sPsl)(75. 2信源符号码符号L

8、)(75. 1)(信源符号比特SH54321,sssssS )(SF)(SF1)(1log)(sPsl00111 .00011110. 00110111. 0)(5 . 3信源符号码符号L43411,0)(21ppsPS11111100S2662)41 ()43() 1 ()0()(PPsP7)(1logsPlsyyPsF)()(111101001001. 082202. 0)43(1)111111(1)11111100()11111101()11111110()11111111(1)(1)111110()11110()1110()110()10()0()(6PPPPPyPPPPPPPsFsy%7 .9287811. 0)(LSH1210,qaaaaAAsssssin321)(lognCl qllog23000113200aaaaaaaaaaa23000113200,aaaaaaaaaaa)()(1)(SHlsPLSHriiirqiiirlpLqiil111min1)()(SHLSHrr2)(SHLr0)(,21iqaPaaaAqiikaPaF1)()(1)(1log)(kkaPal2)(1)(SHLSHsyyPsF)()()(1logsPl